Question: Simplify the following expression: $\dfrac{144k^3}{12k^3}$ You can assume $k \neq 0$.
Explanation: $ \dfrac{144k^3}{12k^3} = \dfrac{144}{12} \cdot \dfrac{k^3}{k^3} $ To simplify $\frac{144}{12}$ , find the greatest common factor (GCD) of $144$ and $12$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(144, 12) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{144}{12} \cdot \dfrac{k^3}{k^3} = \dfrac{12 \cdot 12}{12 \cdot 1} \cdot \dfrac{k^3}{k^3} $ $\phantom{ \dfrac{144}{12} \cdot \dfrac{3}{3}} = 12 \cdot \dfrac{k^3}{k^3} $ $ \dfrac{k^3}{k^3} = \dfrac{k \cdot k \cdot k}{k \cdot k \cdot k} = 1 $ $ 12 \cdot 1 = 12 $